Satya is factorising the polynomial x2 + x - 20 by splitting the middle term. Which of the following should be her first step? (A) x2 + 20x – 19x – 20 (C) x2 + 5x - 4x – 20 (B) x2 – 5x + 4x - 20 (D) x? - 10x + 2x - 20
Answers
Step-by-step explanation:
The factor of a polynomial can be found by splitting the middle term method.
(x – 5) and (x + 4) are the factors of the polynomial x^{2] – x – 20.
The given expression is a quadratic expression. Let's explore the factorization of a quadratic expression.
Explanation:
To find the factors of the polynomial x2 – x – 20, we start with splitting the middle term
The middle term should be split in such a way that the product of the split terms is the same as that of the first term and the constant.
x2 – (5 - 4)x – 20 = x2 – 5x + 4x – 20
= x(x – 5) + 4(x – 5)
= (x – 5) (x + 4)
So, x2 – x – 20 when factored, we get x2 – x – 20 = (x – 5) (x + 4)
Therefore, factors of the polynomial x2 – x – 20 are (x – 5) and (x + 4).
Answer:
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
STEP
1
:
Trying to factor by splitting the middle term
1.1 Factoring x2-x-20
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -20
Step-1 : Multiply the coefficient of the first term by the constant 1 • -20 = -20
Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is -1 .